The Bayes factor for inequality and about equality constrained models

Computational Statistics and Data Analysis

Volumn 51, Issue 12, 2007, Pages 6367-6379

  Klugkist, Irene ^a   Hoijtink, Herbert ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Bayesian model selection; Encompassing prior; Objective bayesian inference; Ordered parameters

Indexed keywords

BAYESIAN NETWORKS; MATHEMATICAL MODELS; OPTIMIZATION; PARAMETER ESTIMATION;

BAYESIAN MODEL SELECTION; ENCOMPASSING PRIOR; OBJECTIVE BAYESIAN INFERENCE; ORDERED PARAMETERS;

CONSTRAINT THEORY;

EID: 34547203118     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.01.024     Document Type: Article

References (39)

1. Agresti A. Analysis of Ordinal Categorical Data (1984), Wiley, New York
2. Agresti A., and Coull B.A. The analysis of contingency tables under inequality constraints. J Statis. Plann. Inference 1-2 (2002) 45-73
3. Akaike H. Factor analysis and AIC. Psychometrika 52 (1987) 317-332
4. Barlow R.E., Bartholomew D.J., Bremner J.M., and Brunk H.D. Statistical Inference Under Order Restrictions (1972), Wiley, New York
5. Berger J.O., and Delampady M. Testing precise hypotheses. Statist. Sci. 2 (1987) 317-352
6. Berger J., and Pericchi L. The intrinsic Bayes factor for model selection and prediction. J. Amer. Statist. Assoc. 91 (1996) 109-122
7. Berger, J., Pericchi, L., 2001. Objective Bayesian methods for model selection: introduction and comparison. In: Lahiri, P. (Ed.), Model Selection. Monograph Series, vol. 38, Institute of Mathematical Statistics Lecture Notes, Beachwood, Ohio, pp. 135-207.
8. Berger J., and Sellke T. Testing of a point null hypothesis: the irreconcilability of significance levels and evidence (with Discussion). J. Amer. Statist. Assoc. 82 (1987) 112-139
9. Bernardo J.M., and Smith A.F.M. Bayesian Theory (1994), Wiley, Chichester
10. Bozdogan H. Model selection and Akaike's information criterion (AIC): the general theory and its analytical extensions. Psychometrika 52 (1987) 345-370
11. Carlin B.P., and Chib S. Bayesian model choice via Markov Chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B 57 (1995) 473-484
12. Carlin B.P., and Louis T.A. Bayes and Empirical Bayes Methods for Data Analysis. second ed. (2000), Chapman & Hall, London
13. Casella G., and Berger R.L. Reconciling Bayesian and frequentist evidence in the one-sided testing problems (with discussion). J. Amer. Statist. Assoc. 82 (1987) 106-111
14. Chen M.H., and Shao Q.M. On Monte Carlo methods for estimating ratios of normalizing constants. Ann. Statist. 25 (1997) 1563-1594
15. Chib S. Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc. 90 (1995) 1313-1321
16. Dawid A.P., and Lauritzen S.L. Compatible prior distributions. In: George E.I. (Ed). Bayesian Methods with Applications to Science, Policy and Official Statistics. Selected Papers from ISBA 2000: The Sixth World Meeting of the International Society for Bayesian Analysis (2001), Eurostat, Luxembourg 109-118
17. Dykstra, R.L., Robertson, T., Silvapulle, M.J. (Eds.), 2002. Statistical inference under inequality constraints [Special issue]. J. Statist. PLann. Inference 107, 1 2.
18. Gelfand A.E., and Dey D. Bayesian model choice: asymptotics and exact calculations. J. Roy. Statist. Soc. Ser. B 56 (1994) 501-514
19. Gelfand A.E., Smith A.F.M., and Lee T. Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling. J. Amer. Statist. Assoc. 87 (1992) 523-532
20. Gelman A., Carlin J.B., Stern H.S., and Rubin D.B. Bayesian Data Analysis (1995), Chapman & Hall, London
21. Green P.J. Reversible jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrika 82 (1995) 711-732
22. Han C., and Carlin B.P. Markov Chain Monte Carlo methods for computing Bayes factors: a comparative review. J. Amer. Statist. Assoc. 96 (2001) 1122-1132
23. Jeffreys H. Theory of Probability. third ed. (1961), Oxford University Press, London
24. Johnson N.L., Kotz S., and Kemp A.W. Univariate Discrete Distributions (1993), Wiley, New York
25. Kass R.E., and Raftery A.E. Bayes factors. J. Amer. Statist. Assoc. 90 (1995) 773-795
26. Klugkist I., Kato B., and Hoijtink H. Bayesian model selection using encompassing priors. Statist. Neerlandica 59 (2005) 5769
27. Lavine M., and Schervish M.J. Bayes factors: what they are and what they are not. Amer. Statist. 53 (1999) 119-122
28. Leucari V., and Consonni G. Compatible Priors for Causal Bayesian Networks. In: Bernardo J.M., Bayarri M.J., Berger J.O., Dawid A.P., Heckerman D., Smith A.F.M., and West M. (Eds). Bayesian Statistics vol. 7 (2003), Clarendon Press, Oxford 597-606
29. Lindley D.V. A statistical paradox. Biometrika 44 (1957) 187-192
30. Moreno E. Objective Bayesian methods for one-sided testing. Test 14 (2005) 181-198
31. Newton M.A., and Raftery A.E. Approximate Bayesian inference by the weighted likelihood bootstrap. J. Roy. Statist. Soc. Ser. B 42 (1994) 213-220
32. Robertson T., Wright F.T., and Dykstra R.L. Order Restricted Statistical Inference (1988), Wiley, New York
33. Roverato A., and Consonni G. Compatible prior distributions for DAG models. J. Roy. Statist. Soc. Ser. B 66 (2004) 47-62
34. Schwarz G. Estimating the dimension of a model. The Ann. Statist. 6 (1978) 461-464
35. Silvapulle M.J., and Sen P.K. Constrained Statistical Inference (2004), Wiley, New York
36. Smith A.F.M., and Roberts G.O. Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B 55 (1993) 3-23
37. Smith A.F.M., and Spiegelharter D.J. Bayes factors and choice criteria for linear models. J. Roy. Statist. Soc. Ser. B 56 (1980) 501-514
38. Snedecor G.W., and Cochran G.C. Statistical methods. sixth ed. (1967), Iowa State University Press, Ames, Iowa
39. Zellner A., and Siow A. Posterior odds ratios for selected regression hypotheses. In: Bernardo J.M., DeGroot M.H., Lindley D.V., and Smith A.F.M. (Eds). Bayesian Statistics (1980), University Press, Valencia 585-603